This article examines eight “gaps” in order to clarify why the quantitative genetics methods of partitioning variation of a trait into heritability and other components has very limited power to show anything clear and useful about genetic and environmental influences, especially for human behaviors and other traits. The first two gaps should be kept open; the others should be bridged or the difficulty of doing so should be acknowledged: 1. Key terms have multiple meanings that are distinct; 2. Statistical patterns are distinct from measurable underlying factors; 3. Translation from statistical analyses to hypotheses about measurable factors is difficult; 4. Predictions based on extrapolations from existing patterns of variation may not match outcomes; 5. The partitioning of variation in human studies does not reliably estimate the intended quantities; 6. Translation from statistical analyses to hypotheses about the measurable factors is even more difficult in light of the possible heterogeneity of underlying genetic or environmental factors; 7. Many steps lie between the analysis of observed traits and interventions based on well-founded claims about the causal influence of genetic or environmental factors; 8. Explanation of variation within groups does not translate to explanation of differences among groups. At the start, I engage readers’ attention with three puzzles that have not been resolved by past debates. The puzzles concern generational increases in IQ test scores, the possibility of underlying heterogeneity, and the translation of methods from selective breeding into human genetics. After discussing the gaps, I present each puzzle in a new light and point to several new puzzles that invite attention from analysts of variation in quantitative genetics and in social science more generally. The article’s critical perspectives on agricultural, laboratory, and human heritability studies are intended to elicit further contributions from readers across the fields of history, philosophy, sociology, and politics of biology and in the sciences.